1. Field of the Invention
The invention relates to a sampling method for sampling signals according to their magnitude but independently of their frequency range, thereby providing more accurate sampling or, from less frequently taken samples, identical quality sampling. Circuitry for accomplishing this method is also disclosed.
2. Description of the Prior Art
Sampling methods of several kinds and several circuit arrangements for the realization of these methods are known from literature and practice.
Essentially, sampling methods are divided in three groups by Alfred I. Monroe (Digital Processes for Sampled Data Systems, John Wiley and Sons, Inc., New York, 1962) and Frigyes Csaki (Regulation Dynamics, Akademiai Kiado, Budapest, 1970).
The most frequently used subgroup of fixed sequence linear sampling is known as simple (or common) sampling. Samples are taken at very short, constant intervals. Hence, the series of samples may be considered as a series of pulses. This method is described in detail in Chapter 15.5 ("Sampling Systems") of the book by Francis H. Raven, Automatic Regulation (Muszaki konyvkiado, Budapest, 1965).
In Hungarian patent specification No. 168/55 a method is described for the measurement and recording of periodically sampled, rapidly changing cyclical signals. This method offers the possibility of measuring all required samples from a minimum number of cycles by taking the samples in the most expedient order of sequence and reestablishing their original sequence for the purpose of storage. According to this method, samples are taken at every n-th place of the identifying signal sequence and the number of the identifying signal sequence selecting the number of the sampling signal chosen from these, so as to make the two numbers contain different prime factors only. Then the samples thus measured are stored in the memory of address m.sub.i corresponding to the serial number of the identifying signal sequence. The voltage U to be measured is connected to the input of an A/D converter. The identifying pulses are led to the other input of the A/D converter through a pulse division circuit. After zeroing, the pulse division circuit issues a pulse to start a sampling under the effect of the first and all subsequent p-th pulses. Under the effect of each such pulse a pulse sequence proportional to the instantaneous value of voltage U is transferred from the A/D converter (instantaneous value meter) to the counter. At the end of conversion, under the effect of the pulse taken from the A/D converter the content of the counter is discharged into the register located at the first memory address. After the storage cycle the address register of the memory is shifted by a shift pulse by p steps, said shifting pulse being issued responsive to a voltage pulse by a second counter with the help of a clock generator. The address shifting pulses are counted by means of a cycle counter. When the number of address shift pulses reaches that of the identification signal sequence, a voltage signal is issued by the cycle counter to cause zeroing of the address register and itself, so that the address register is stepped forward from its zeroed state by means of the pulses left over from those of number p.
Also based on a sampling method of equal time intervals is the electronic circuit described in another Hungarian patent specification, No. 174,408, devised for amplification of analog sample signals with coefficients assuming discrete values.
Sometimes displaced (delayed or accelerated) sampling is used. In such cases, input and output signals are sampled at equal intervals t, but displaced by an interval T with respect to each other. This method is adapted mainly to multivariable time-sharing samplings. When sampling takes place cyclically at variable intervals the sampling interval varies cyclically, e.g. sinusoidally.
In the case of aperiodic sampling the sampling interval varies, but this variation is not cyclical. For example, with intermittent aperiodic sampling samples are taken at intervals T, but not at every such interval.
With slowly changing aperiodic sampling the interval between successive samplings varies, but only slightly.
With sampling taken at intervals changing after certain periods the interval T changes, but remains constant within said periods.
To the other subgroup belongs linear sampling of finite duration. Instantaneous taking of the samples is an approximation only; in reality, the samples are taken during a finite duration. Such a linear sampling of finite duration is realized by the circuit arrangement described in Hungarian patent specification No. 176,618 for the sampling of analog signals.
The other group of sampling is non-linear sampling. If changing of the sampling process does not take place according to a predetermined rule, but depends on the magnitude of the signal, the sampling is classified as non-linear. In Hungarian patent specification No. 172,590 an adaptive sampling circuit arrangement is described. Such adaptive sampling can be adapted to all cases where samples are to be taken from analog signals. Two wide fields of application are represented by the sampling (computer-based) regulation and telecommunication signal transmission. The method consists essentially of taking a new sample from analog signals to be transmitted only when the state of signals (or system, e.g. regulation) exhibits a definite change with respect to the value obtained by the preceding sample.
From the sampling criteria certain sampling laws can be deduced. These laws are mathematical formulae, from which the approximate duration of the sampling interval can be directly found, using the values obtained from the last sampling. In this way the lengths T.sub.i of the sampling intervals can be determined from the sampling criteria only if approximate assumptions are made as to how the signal (system) will vary, and the convention stated in criterion is satisfied only approximately. Additionally, a digital computer is required for evaluation of the formula obtained for the lengths of the sampling interval since discrete signal values have to be processed.
From the sampling criteria given in the mathematical formulae of the above patent specification, the lengths of sampling intervals are obtained by extrapolating the values of the last few sampled signals. This is a means through which the time of the next sampling can be assessed by means of discrete signal processing (e.g. with the use of a microprocessor). In the adaptive circuit arrangement proposed by the above-mentioned specification in the sequence of signal transmission, a difference amplifier, an absolute value former, an integrator, a comparator and a two-input OR-gate are connected in series. To one input of the difference amplifier are connected the input of the samples and self-reading circuit, to its other input the samples and self-sealing circuit or some other signal sources proportional to the latter are connected, whereas the output of pulse shaping circuit is led to the timing circuit causing the initial zero setting of the integrator to switch over into its other state after the elapse of a definite time, and the output of the reference-signal generator in the case of obtaining from the comparator a reference signal varying as a function of time producing a suitable reference signal is coupled to the reference input of the comparator, whereas the output of the timing circuit is linked up with one of the inputs of the OR-gate.
The third group of sampling is the semi-random, so-called Monte Carlo method, consisting of taking at random samples of discrete signal values. This method is suitable for recording statistical data occurring at random steady-state intervals, such as signals.
With the equal-interval sampling, about 99% of the time the signal components exceeding the Nyquist frequency do not pass by the sampling circuit and the components are recorded with different errors depending on their frequency. With signals of wide frequency spectra the number of samples taken will be lower than necessary in the upper range of frequencies but higher than necessary in the lower ranges. Owing to the frequency limitations, this kind of sampling is incapable of transmitting sections of signals where the rate of rise exceeds the maximum steepness determined by the sampling interval T.
Samplings taken at varying intervals can only partly overcome the above disadvantages, and offer no satisfactory solution in general. Frequency limitation is also imposed here, and the criterion of optimization cannot be satisfied. Sampling of an arbitrary signal, unknown in advance, thus cannot reliably be recorded.
These sampling methods can effectively be performed only in cases where the laws defining the signal shape are known in advance.
In the case of processes of wide frequency ranges and lasting much longer than the cycle time of the highest frequency component, such sampling methods may result in a very high number of superfluous samplings.
Although this effect is considerably reduced by the linear adaptive sampling mentioned above, this method still has the drawback of requiring the performance of additional calculations for determining the time of the next sampling, based on using the value of preceding samplings. The sampled value and also the time of sampling has to be determined and stored. A further considerable problem consists of requiring separate circuit arrangements for satisfying each item of the various criteria, as well as the inability of these circuits to transmit signal sections having rates of rise which exceed a certain steepness, or to recognize vertical or near-vertical signal sections. RAndom sampling is similarly unsuited for safely taking samples, since this method lends itself only to recording statistical characteristics of processes of a steady-state nature in time with relatively fair accuracy, but it does not permit true-to-form recording of the signal. Moreover, it may decisively distort the deterministic signal portions.
An attempt to eliminate the drawbacks of sampling methods widely used in practice has been made by HINZ in U.S. Pat. No. 4,291,299, in which a sampling system (A/D converter) is specified representing an intermediate technology between the methods of adaptive sampling and sampling according to the value of samples.
The above system essentially consists of leading the sampled signal, on the one hand, to a conventional sampling (sample and hold) circuit by which at each instant of sampling to be recorded a sample is taken from the signal and stored until a new sample is taken for storage. On the other hand, the sampled signal is fed into a so-called first comparator chain the comparators of which indicate when a preset voltage level is reached by the signal. Additionally, a difference-forming unit determines the difference between the instantaneous value of the input signal and the value of the signal at the instant of the preceding sampling (stored by the sample-and-hold circuit), and this difference is led to a so-called second chain of comparators, which indicates the time when the value of the signal changes to assume a predetermined value.
As a result of this method, sampling is effected at the time differences elapsing between consecutive instances at which the magnitude of the signal reaches a predetermined value, or the difference between instantaneous and preceding signal magnitudes exceeds predetermined value.
This known solution utilizes for sampling the principle of comparator monitoring already known and widely used in other fields of application. U.S. Pat. Nos. 3,657,646 (Zmyslowski), 3,298,014 (Stephenson), 3,903,470 (Mirabile), 4,152,642 (Dohety) and 4,210,904 (Renzel) are mentioned in this regard, by virtue of which the sampling of signals is rendered possible over a wider frequency range than is possible with conventional sampling systems.
From the patents listed above, Stephenson has devised a type of A/D converter by which signal magnitudes can be determined. A general feature of the other above references is their use in determining certain derived parameters, and not for the purpose of sampling.
For example the patent to Zmyslowski is a signal analyzer (and not a sampling device) for performing four functions on the incoming signal: determining its interference coefficient, average crest value and pulse groups, and plotting their numerical values along a graduated linear scale. From the quantities determined by the equipment--these representing average information characteristic of a given section of the train of signals--the signal itself could not be reconstructed even if the information were stored, which is not done by this equipment, being beyond the scope of the patent.
In the patent of Hinz, referred to above, this is accomplished by organizing the sampling in an adaptive way, so that with each formation of the signal value a conventional sample and hold circuit is controlled by feedback, and the instant at which an average level is reached by the signal or at which an average level is exceeded by the signal change, is monitored by means of comparators, and when either of said conditions occurs, the code of the level surpassed, together with the time that has elapsed since the preceding sampling, are recorded as a sampled value.
In spite of the advantage offered by Hinz as compared to conventional sampling methods, numerous other features inherent in Hinz represent drawbacks in its wide-range application. Specifically:
1. The equipment is nonetheless unsuitable for sampling signals of unrestricted frequency range, because although the transmitted upper frequency limit is rather high, the system is unable to transmit frequencies above this limit. The procedure used for forming sample values is complicated. The resulting complexity prolongs the transfer time of the system, determining an upper frequency fN beyond which the equipment fails to record.
2. For a sufficiently accurate sampling according to the signal value, say, at 8-bit (256-level) resolution, the number of component (e.g. of comparators, monostables, coders) that must be incorporated in the equipment becomes excessively high, rendering the setup too complex and costly.
3. With the sampling accomplished by this equipment considerable errors may arise, owing to the required feedback to the "sample and hold circuit" after each sampling. The source of these errors lies in the inherent delay causing discontinuities in the transmission. This delay is the result of the time required by the equipment to decide whether a signal received at its input has satisfied, or not, the criteria (level crossing and difference checkings). The "sample and hold" circuit will be instructed by the equipment to perform a further sampling only if this criteria has been fulfilled, yet at this instant the value of the signal will no longer be the same [value of signal at instant (t) versus value of signal at instant (t+DT)], where DT is the transmission (dead) time of the feedback of the equipment. This may cause even very large errors, if the signal happens to change during transmission time DT because the criterion is found to be fulfilled for the signal input at instant (t), whereas the equipment will use the quantity of signal value prevailing at instant (t+DT) as the basis for further sampling.
This is all the more disadvantageous, since the previous obvious error can be expected to occur with nearly all samplings, so that a given error will be carried over to all subsequent samplings.
The source of the above disadvantage lies in utilizing the "sample and hold circuit" as an essential element of the sampling equipment and in treating adaptively the amount of change taking place in the value as critical information.
4. The value of the monitored levels is rigidly fixed within a given equipment, and this can be modified only by setting up newly designed equipment, owing to dimensioning problems.
5. The time intervals between successive samplings are recorded, as the equipment is incapable of recording the instants of samplings along a so-called absolute time scale commencing at an arbitrarily chosen instant t.sub.o =0, which should be in many cases a desirable final aim when resetting is to be performed. The data sampled by means of this equipment (by which so-called relative times are recorded) thus often have to be subsequently converted into absolute times, which may further distort the results due to the errors indicated in item 2. above, and to errors arising from said conversion.
6. Besides the time data, recording of the level code is required in any case, thereby unnecessarily increasing the storage capacity required for the sampling.
7. It may occur that, at an instant of sampling, a signal is found to be greater than or equal to a predetermined level and, at the same time, differ by a determined value from the previous sampling. In this case, the first and second chains of comparators may give indications at the same instant, giving rise to priority problems requiring the use of priority coding circuits, whereby the complexity, cost and operating time is further increased.
8. Considering their function, the elements of the second chain of comparators (.+-.0.1 V, .+-.0.3 V, .+-.1 V) are of reduced value from the point of view of sampling, since they serve only for monitoring the deviation of the signal from its previously sampled value. This may introduce serious errors in the sampling process, since if such a comparator becomes active, this brings it, at the same time, into a condition that will prevent it from becoming active again, until the signal value changes with respect to its own comparing level.
To illustrate the above disadvantage, if the analog signal intersects, in any direction, the monitoring level defined by the comparing level of a second comparator, after which the direction of the signal changes before reaching the adjacent monitoring level, and again passes across the monitoring level defined by the second comparator, at which the previous sampling took place, no repeated sampling will occur, for the signal has not changed on the difference amplifier with respect to the previous sampling. Thus, if at the monitoring level defined by the second comparators several samplings would occur in succession, only the first of them would be retained by the Hinz method. This, however, will considerably distort the signal and falsify with respect to the original signal the frequency content of the reconstructed signal. And, what is worse, this loss of information is uncontrollable, because with the first comparators and with the second comparators following the first, the error in the value of sampling is determined by the spacing between adjacent monitoring levels, whereas with the levels that follow defined by the second comparators owing to the dynamic difference formation, the error is influenced by the double spacing between monitoring levels.
Since, in the case of an unknown signal, the above mentioned events may follow each other in undefined succession, in some sections of the signal the frequencies appearing with half amplitude will also be recorded, whereas in other sections even the frequencies appearing with the double of these amplitudes become blurred. The error in signal recording is thus accidental and unforeseeable, and the frequency range and shape of the recorded signal will also become considerably distorted. The statements described in the foregoing are illustrated in FIG. 16: FIG. 16a shows an analog signal to be recorded, and FIG. 16b shows the result of sampling performed with Hinz's A/D converter. It is apparent that, owing to dynamic difference forming and to the function of the second comparators described above, the shape and frequency content of the sampled signal has become very much distorted as compared to the original, even disregarding the effect of drawback No. 3. above (changing of the analog signal during feedback), by which the signal would suffer further distortion.
Owing to the disadvantages discussed above, the equipment proposed by Hinz is unsuited for many practical applications.
Let us, for example, consider the case of the Induced Polarization (I.P.) Geophysical method, where a geological medium or certain substances are classified according to their excitability and the technical arrangement of measurement is as follows. Turning now to FIG. 13a, a current pulse of TG duration is injected into the soil between electrodes A and B, and the variation of voltage response as a function of time is monitored between two other points (M, N) of the soil.
The variation of the excitation current pulse as a function of time is shown in FIG. 14a, while that of the voltage response measured between electrodes M, N is illustrated in FIG. 14b.
If the coupling provided by the soil were replaced by purely ohmic members, then a voltage pulse appearing between electrodes M and N would be synchronous with the injected current pulse. The medium, however, will most often not be substituted by purely ohmic members, and therefore it will be found (as shown in FIG. 14b) that the voltage between electrodes M and N gradually approaches a maximum value and, after disconnecting the excitation current, a gradually decaying transient signal will be measured.
When the phenomenon described above is found to occur across electrodes M and N, the medium is termed polarizable. In order to determine material composition and geometry of the medium, however, the transient response signal must be accurately known. A similar response signal is obtained when, in the arrangement of FIG. 13b the composition of a material sample is investigated by the IP method. The frequency range of this transient response signal, however, is very wide, and at the instant of disconnection the signal changes from a value of U(TG) to the value of .DELTA.U(O) as shown in FIG. 14b, and this change shows just the effect of the conductive members. Thus, a component of infinitely high frequency appears, followed by the transient decay of the signal, so that the effect of higher frequencies decreases and the effect of lower frequencies gradually becomes dominating right down to DC level. This produces a wide frequency spectrum, in which--ranging from 0 Hz (DC level)--the various frequencies are gradually present up to the infinitely high-frequency (voltage jump) component.
Moreover, the value .DELTA.U(O) recorded at the instant of disconnection would be a very important parameter with the IP-method, the value of which, however, cannot be determined by means of conventional sampling methods. Namely, if the equally spaced sampling system is adapted, it will be incapable of recording the first high-frequency section of the signal, whereas in the subsequent low-frequency sections it will supply an increasing number of unnecessary (superfluous) samplings.
Unfortunately, the conditions demanded by the IP-method cannot be solved by means of Hinz's sampling equipment either, since--as described above--due to the transmission dead time of the system, the Hinz equipment is similarly incapable of transmitting frequencies higher than a certain upper frequency, thus rendering it unsuitable for use in determination of the very important .DELTA.U(O) parameter and that of the first high-frequency section of the curve.
Since for evaluation by means of the IP method accurate recording of the entire transient response signal is needed, the monitoring levels have to be chosen so as to be sufficiently dense in the range of values of the signal, and thus disadvantage No. 2. of the Hinz equipment appears here, where the demand in components grows excessively and renders the equipment too complicated. Since a continuously decaying signal is produced by the transient process, it will surely be true that the signal will change after every sampling, so that disadvantage No. 3. of the Hinz equipment appears here as such a sampling error, due to the dead time of feedback, which--owing to its additive nature--causes the distortion of the entire signal, creates distortion that increases gradually with increasing frequencies within the high-frequency section of the spectrum. With IP measurements, in the various material tests and fill measurements, the amplitude of response voltage may assume widely varying values, thus rendering necessary sampling equipment in which the value of monitoring levels can flexibly be varied. Here, drawback No. 4. of the Hinz equipment manifests itself.
The essential mathematical feature in evaluating the IP-method is that the instant of disconnection the excitation current pulse is taken as initial time t.sub.o =0, and at every subsequent sampling the time that has elapsed since the instant of disconnection is of interest. Here, drawback No. 5. of the Hinz equipment appears, according to which the time intervals between two samplings are recorded, which thus does not immediately provide an absolute time. As a result, the sampled values cannot be directly utilized in IP-evaluation, but instead require conversion to absolute time data, increasing the time requirement and cost of evaluation. Moreover, due to the errors resulting from the transmission dead time mentioned under disadvantage No. 2. above, this conversion becomes the source of further errors, as a consequence of the laws governing the propagation of errors.
For recording the transient response signal of the IP method by means of the Hinz method the code of the monitor level is, of course, required, meaning that, due to drawback No. 6. above, this necessitates a larger storage capacity. With recording of the response signal of the IP-transient by means of the Hinz equipment, the problem of ambiguity described above under drawback No. 7. may also arise, due to the frequency of the signal varying from instant to instant.
Some of the drawbacks outlined in the foregoing also appear in other fields of application. Generally, for a given signal shape to be analyzed, accuracy of signal recording is of basic importance, but even the recognition of a simple step function (component of infinite frequency) cannot be achieved either with conventional techniques or--as shown--with the Hinz equipment.
As the signal shape analyzers require very accurate recording of signals, so the disturbing effects of errors resulting from the transmission delay and an increase of complexity of the Hinz equipment also appears here. Another field of application of this kind is the magneto-tellurical geophysical method (magneto-tellurics), where random electromagnetic Waves of various frequencies present in the atmosphere are utilized for detecting vertical stratifications of the earth. Here random signals are to be recorded, in which the useful information is carried also by a wide frequency spectrum. Besides these, in all fields of signal recording and processing the deficiencies of methods of distributed sampling, including those of the Hinz method have to be faced, where wide-spectrum signals unknown in advance are to be safely recorded at a given accuracy while requiring minimum storage capacity.
In the following a sampling method and a sampling equipment (A/D converter) for its accomplishment will be described, by means of which the deficiencies of conventional sampling methods (gapless recording--loss of components of certain frequencies as a result of sampling, unnecessarily large storage capacity) and the drawbacks of the Hinz equipment described above can be eliminated.